Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Solution{

    static int findMinInRow(int[][] g, int i){
        int min = g[i][0];

        for(int j=0; j<g[i].length; j++)
            min = Math.min(min, g[i][j]);

        return min;
    }

    static int findMinInCol(int[][] g, int j){
        int min = g[0][j];

        for(int i=0; i<g.length; i++)
            min = Math.min(min, g[i][j]);

        return min;
    }

    static int handleRows(int n, int m, int[][] g, StringBuilder sb){
        int steps = 0;

        int min;
        for (int i=0; i<n; i++){
            min = findMinInRow(g, i);

            for(int j=0; j<m; j++)
                g[i][j] -= min;

            for(int j=0; j<min; j++)
                sb.append("row " + (i+1) + "\n");
            steps += min;
        }

        return steps;
    }

    static int handleCols(int n, int m, int[][] g, StringBuilder sb){
        int min;
        int steps = 0;

        for (int j=0; j<m; j++){
            min = findMinInCol(g, j);

            for(int i=0; i<n; i++)
                g[i][j] -= min;

            for(int i=0; i<min; i++)
                sb.append("col " + (j+1) + "\n");

            steps += min;
        }

        return steps;
    }


    static String solve(int n, int m, int[][]g){
        StringBuilder sb = new StringBuilder();
        int steps = 0;

        if (n < m){
            steps += handleRows(n, m, g, sb);
            steps += handleCols(n, m, g, sb);
        } else {
            steps += handleCols(n, m, g, sb);
            steps += handleRows(n, m, g, sb);
        }

        for(int i=0; i<n; i++)
            for(int j=0; j<m; j++)
                if(g[i][j] != 0)    return "-1";


        return steps + "\n" +sb.toString().trim();
    }

    public static void readInputPrintOutput(Escanner sc, PrintWriter out) throws Throwable{
        int n = sc.nextInt();
        int m = sc.nextInt();

        int[][] g = new int[n][m];
        for(int i=0; i<n; i++)
            for (int j=0; j<m; j++)
                g[i][j] = sc.nextInt();

        String ans = solve(n, m ,g);
        out.print(ans);
    }

    public static void main(String[] args)throws Throwable{
        Escanner sc = new Escanner();
        out = new PrintWriter(System.out);
        /////
        readInputPrintOutput(sc, out);
        /////
        out.close();
    }
    static class Escanner {
        BufferedReader in;
        StringTokenizer st;

        Escanner() throws Throwable {
            in = new BufferedReader(new InputStreamReader(System.in), 32768);
            st = new StringTokenizer("");
        }

        Escanner(String fileName) throws Throwable {
            in = new BufferedReader(new FileReader(fileName),32768);
            st = new StringTokenizer("");
        }

        boolean isBlank() throws Throwable{
            String l = in.readLine();
            st = new StringTokenizer(l==null?"":l);
            return !st.hasMoreTokens();
        }

        boolean EOL(){
            return !st.hasMoreTokens();
        }

        String nextStr() throws Throwable {
            while(!st.hasMoreTokens())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        int nextInt() throws Throwable {
            return Integer.parseInt(nextStr());
        }

        long nextLong() throws Throwable {
            return Long.parseLong(nextStr());
        }

        BigInteger nextBigInt() throws Throwable {
            return new BigInteger(nextStr());
        }

        double nextDouble() throws Throwable {
            return Double.parseDouble(nextStr());
        }
    }
    static PrintWriter out;
}